天生桥一级水电站溢洪道掺气减蚀研究
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摘要
长期以来,空化现象被认为是一不易被解决的问题。空化与空蚀的研究,无论从国际或国内动态来分析,近年来均呈现备受重视和日益深入的趋势。不仅国际国内学术交流频繁,更重要的是工程问题较多,研究内容随之不断扩展,涉及领域拓宽,业已成为众多行业共同关注的问题之一。
国内外的研究情况表明,对空化和空蚀机理及其影响因素的认识和研究已取得很大进展。应该指出的是,由于空化和空蚀是微观、瞬时、随机、多相的复杂现象,到目前为止,有关空化和空蚀的理论及不少研究成果还不能令人满意,许多问题还有待进一步深入研究和探索。
工程经验表明,掺气减蚀是防止溢洪道空蚀的重要措施,根据国内科研机构几座在建或已建大型工程的试验研究发现,合理掺气设施的设置可以达到比较理想的掺气效果。目前,大多在建、拟建或已建的大型泄洪建筑物中,几乎都设置了掺气减蚀设施,但基本上都是掺气设施的工程实践在先,而相应的掺气减蚀机理研究和模型试验则相对滞后。故目前有关掺气设施的各项水力指标的设计和计算多依赖于经验关系和定性的研究,理论方面的研究比较少。
本文针对溢洪道的空化空蚀及掺气减蚀问题,在前人工作的基础上,结合天生桥一级水电站溢洪道工程实例,对高水头大泄量溢洪道的空化空蚀问题及掺气减蚀进行了研究,通过模型试验,提出了合适的掺气槽体型,可以方便工程的施工,保证施工质量,最大限度减少空化空蚀,提高了溢洪道泄槽的安全度。
For a long time, the cavitation phenomenon is considered being a problem hard to be solved. Cavitation and the research on it, no matter we analyse it from international or domestic, it has being taken seriously attention and has a gradually thorough trend on it.Not only the academic exchange is more and more, but also there are many engineering problems on it, study content of the problem is broadening, expanding, it has also becoming one of the problem that many relating industry pay attentions to.
The domestic and international research circumstances indicate that, study on cavitation and cavitation errosion mechanism and their influencing factors have got a great progress already. But we must point out that, since cavitation and the cavitation errosion is a complicated phenomenon such as microcosmic, instant, random and heterogeneous,by now, theory and many research result about cavitation and cavitation errosion can not all be desired , a lot of problem remains to further study and probed in a deepgoing way.
The engineering experience indicates that, aerator is an important measure to provent cavitation errosion for flood spillway, according to the research and model test taken by domestic institute on some in building or already building large-scale flood spillway , the reasonable setting of aerator can get a perfect aeration effect. At present, aeration facilities are set up to almost all the in building or already building large-scale flood discharging bulding, however, basically the practice of aerator is prior, the corresponding research and model tests of aeration facilities are relative lagging. Accordingly, the design of hydraulic characteristic and calculation of aeration facilities is mainly dependent on experience and qualitative research, the research in theory aspect is comparatively few.
Based on former study of others, this paper is basically aim at the problem of cavitation and cavitation erosion and aeration facilities for proventing cavitation erosion. Associate with the project example of the flood spillway of Tian shengqiao 1 hydropower station, carried on a research mainly to the cavitation and cavitation errosion and aeration mitigation and their application in the flood spillway with high head and huge discharge.The applied shapes of the aerator’s which were suitable to the project, this kind of design is convenient to project construction, ensure the construction quality, reduced the cavitation erosion and increase the safety degree of flood spillway.
国内外的研究情况表明,对空化和空蚀机理及其影响因素的认识和研究已取得很大进展。应该指出的是,由于空化和空蚀是微观、瞬时、随机、多相的复杂现象,到目前为止,有关空化和空蚀的理论及不少研究成果还不能令人满意,许多问题还有待进一步深入研究和探索。
工程经验表明,掺气减蚀是防止溢洪道空蚀的重要措施,根据国内科研机构几座在建或已建大型工程的试验研究发现,合理掺气设施的设置可以达到比较理想的掺气效果。目前,大多在建、拟建或已建的大型泄洪建筑物中,几乎都设置了掺气减蚀设施,但基本上都是掺气设施的工程实践在先,而相应的掺气减蚀机理研究和模型试验则相对滞后。故目前有关掺气设施的各项水力指标的设计和计算多依赖于经验关系和定性的研究,理论方面的研究比较少。
本文针对溢洪道的空化空蚀及掺气减蚀问题,在前人工作的基础上,结合天生桥一级水电站溢洪道工程实例,对高水头大泄量溢洪道的空化空蚀问题及掺气减蚀进行了研究,通过模型试验,提出了合适的掺气槽体型,可以方便工程的施工,保证施工质量,最大限度减少空化空蚀,提高了溢洪道泄槽的安全度。
For a long time, the cavitation phenomenon is considered being a problem hard to be solved. Cavitation and the research on it, no matter we analyse it from international or domestic, it has being taken seriously attention and has a gradually thorough trend on it.Not only the academic exchange is more and more, but also there are many engineering problems on it, study content of the problem is broadening, expanding, it has also becoming one of the problem that many relating industry pay attentions to.
The domestic and international research circumstances indicate that, study on cavitation and cavitation errosion mechanism and their influencing factors have got a great progress already. But we must point out that, since cavitation and the cavitation errosion is a complicated phenomenon such as microcosmic, instant, random and heterogeneous,by now, theory and many research result about cavitation and cavitation errosion can not all be desired , a lot of problem remains to further study and probed in a deepgoing way.
The engineering experience indicates that, aerator is an important measure to provent cavitation errosion for flood spillway, according to the research and model test taken by domestic institute on some in building or already building large-scale flood spillway , the reasonable setting of aerator can get a perfect aeration effect. At present, aeration facilities are set up to almost all the in building or already building large-scale flood discharging bulding, however, basically the practice of aerator is prior, the corresponding research and model tests of aeration facilities are relative lagging. Accordingly, the design of hydraulic characteristic and calculation of aeration facilities is mainly dependent on experience and qualitative research, the research in theory aspect is comparatively few.
Based on former study of others, this paper is basically aim at the problem of cavitation and cavitation erosion and aeration facilities for proventing cavitation erosion. Associate with the project example of the flood spillway of Tian shengqiao 1 hydropower station, carried on a research mainly to the cavitation and cavitation errosion and aeration mitigation and their application in the flood spillway with high head and huge discharge.The applied shapes of the aerator’s which were suitable to the project, this kind of design is convenient to project construction, ensure the construction quality, reduced the cavitation erosion and increase the safety degree of flood spillway.
引文
[1]陈椿庭.关于高坝泄洪消能的若干进展.水工水力学及水文论文集.水利电力出版社.1993年10月.
[2] Knapp.Daily.Hammitt.Cavitation.McGraw—Hill.1970.(中译本.空化与空蚀。水利出版社.1981年) .
[3]郭军等.大型泄洪洞高速水流的研究进展及风险分析[J].水力学报.2006年第10期.
[4]吴持恭,高速水力学学科发展综述[J],泄水工程高速水流研究进展,1990,年10月.
[5] Besant,H.W., Hydrostatics and Hydro dynamics, Art.158, Cambridge University Press, London, 1859.
[6] Rayleigh, L., On the Pressure Developed in a Liquid During the Collapse of a Spherical Cavity, Phil. Mag. Vol.34, 1917.
[7] Plesset, M.S., The Dynamics of Cavitation Bubbles[J], Trans. AS ME, J.Appl. Mech., vol.16, 1949.
[8] Gilmore, F.B., The Growth and Collapse of a Spherical Bubble in a Viscous Compressible Liquid, Calif. Inst. of Tech., Hydrodyn. Lab., Rep. 26-4, 1952.
[9] Benjamin, T.B., Pressure Waves From Collapsing Cavity, 2nd Symp. Naval Hydrodyn., Washington D.C., 1958.
[10] Hunter, C., On the Callapse of An Empty Cavity in Water, J. Fluid Mech., Vol.8, 1960.
[11] Hickling, R., Plesset, M.S., Collapse and Rebound of A Spherical Bubble in Water, Phys. Fluids, Vol.7, 1964.
[12] Jahsman, W.E., Collapse of A Gas-Filled Spherical Cavity, J. Appl. Mech., vol.35, 1968.
[13] Plesset, M.S., Prosperetti, A Bubble Dynamics and Cavitation, Annual Revew. of Fluid Mech., Vol.9, 1977.
[14] Naude, C.F., Ellis, A.T., On the Mechanism of Cavitation Damage by Nonhemispherical Cavities Collapsing in Contact with a Solid Boundary, Trans ASME, J. Basic Engr., Vol.83, 1961.
[15] Van wijingaarden, L., On the Collective Collapse of A Large Number of Gas Bubbles in Water, Proc. 11th Int. Congr. of Appl. Mech., Springer, Berlin, 1964.
[16] Chahine, G.L., Asymptotic Theory of Collective Bubble Growth and Collapse, Proc. 5th Int. Symp. On Water Column Separation, Obernach, Germany, 1981.
[17] Morch, K.A., Cavity Cluster Dynamics and Cavitation Erosion, Report of Appl. Phy. Lab., Technical University of Denmark, DK-2800, Lyngby, Denmark, 1982.
[18]黄建波,初生空化数及空化荷载的预测[D].博士论文,大连理工大学,1987年9月.
[19] Plesset, M.S., Chapman, R.B., Collapse of An Initially Spherical Vapor Cavity in the Neighbourhood of A Solid Boundary, J.Fluid Mech., Vol.47, 1971.
[20] Mitchell, T.M & Hammitt, F.G. Asymmetric Cavitation Bubble Collapse [J]. Trans. ASME, J.Fluids Eng. 1973, 95,29-37.
[21] Guetti,L., Lucca.G & Prosperetti A. A Numerical Method for the Dynamics of Non-spherical Cavitation Bubbles. In Proceedings of the 2nd International colloquium on drops and bubbles[C],1981,175-181.
[22]陆力,许协和,固液两项流体中刚性平面边壁附近的空泡溃灭计算[J],水动力学研究与进展,1990年12月,106-119.
[23]蔡悦斌,鲁传敬,何友声,瞬态空化泡的成长与溃灭[J],水动力学研究与进展,1995年12月,653-660.
[24]丁志杰,张慧生,数值模拟气泡在粘性液体中上升运动的Euler-Lagrange方法[J],复旦大学学报自然科学版,1999,Vol 038,No002,146-152.
[25]严育兵,边界积分法的若干问题和近壁空化气泡表面张力效应的数值研究[D],复旦大学博士论文,2002.
[26] R.T.Knapp, J.W.Daily, and F.G. Hammitt,“Cavitation”,McGraw Hill Book Book Co., 1970.中译本“空化与空蚀”[M],水利水电科学研究院译,水利出版社,1981年.
[27] F.E. Fox and K.F. Herzfeld,“Gas Bubbles with Organic Skin as Cavitation Nuclei”, Jr. Acoust. Soc. Am. 26, 1954.
[28]常近时,寿梅华,于希哲,“水轮机运行”[M],水利电力出版社,1983年.
[29] E.N.Harvey, W.D.McElroy and A.H. Whiteley,“On Cavity Formation in Water”, Jr. Appl. Phys., 18, No.2, 1947.
[30] Hall, J.W., The Inception of Cavitation on Isolated Surface Irregularies, Trans. ASME, Basic Engr. Vol.82, 1960.
[31] Arakeri, V.H., Acosta, A.J., Viscous Effects in the Inception of Cavition on Axisymmetric Bodies, Fluids Engr., Trans ASME, Vol.95, 1973.
[32] Katz, J., Cavitation Phenomena with Regions of Flow Separation, J.Fluid Mech., Vol.140, 1984.
[33] Keller, A.P., Cavitation Investigations at Model Body Families as A Contribution to the Classification of Scale Effects at Cavitation Inception, Int. Symp. on Hydraulics for High Dam, Beijing, Nov. 1988.
[34]何子干,紊流场的计算及初生空化数的理论预测[D],博士论文,大连理工大学,1988年8月.
[35]杨庆,空化初生机理及比尺效应研究[D],博士论文,四川大学,2005年5月.
[36] M.Kornfeld and L.Suvarov,“On the Destructive Action of Cavitation”, Jr.Appl.phys., 15,1944.
[37] M.Rattray,“Perturbation effects in Cavitation Bubble Dynamics”, Ph.D.thesis Calif Inst. Of Technology, Pesadena, Calif, 1951.
[38] C.F.Kling and F.G.Hammitt,“A Photograph Study of Spark Induced Cavitation Bubble Collapse”, Trans. ASME, J. Basic. Engr., Vol.94, Ser. D., No.4, Dec. 1972.
[39] W.Lauterborn and H. Bolle,“Experimental Investigations of Cavitation Bubble Collapse in the Neighbourhood of a Solid Boundary”, J. Fluid Mech, Vol.72, No.2,1975.
[40] A.Shima, K.Takayama and Y.Tomita,“Mechanisms of the Bubble Collapse Near a Solid Wall and the Induced Impact Pressure Generation”, Rep Inst. High Speed Mech. Vol. 48,1984.
[41] A.T.Ellis,“Production of Accelerated Cavitation Damage by an Acoustic Field in a Cylindrical Cavity”, Jr. Acoust. Soc. Am., 27, 1965.
[42] G.Petracchi,“Investigations of Cavitation Corrosion”, Metallurgia Italiana, 4l, No. 1, 1949.
[43] M.S.Plesset,“Bubble Dyramics”, in R. Davies (ed.), Cavitation in Real Fluids, Elsevier Publishing Co., Amsterdam. 1964.
[44] W.S.汉密尔顿,水工建筑物气蚀破坏与防护[J],中南水电,1989年第3期.
[45]熊贤禄,傅佩芬整理,美国专家布格和蒋赛延关于二滩水电站水力学问题的发言(综合整理)[J],水电工程研究,1983(1).
[46]溢洪道设计规范[S],SL253-2000.
[47] Mousson J.M., Pitting Resistance of Metals Under Cavitation Conditions, Trans, ASME, 59,1937.
[48] Vuskovic I., Recherches Concernant L′inbluenc de la Teneur en Air la Cavitation et la Corrosion, Bulletin Escher-Wyss, Tom. 13, 1940.
[49] Peterka A.J., The Effect of Entrained Air on Cavitation Pitting, Proc. IHR Minnesota, 1953.
[50] Rasmussen R.E.H., Some Experiments on Cavitation Erosion in Water mixed with Air, Proc. NPI. Sympoaium on Cavitation in Hrdrodynamics, Paper 20, London. 1956.
[51] Russell S.O. and Sheehan G.J., Effect of Entrained Air on Cavitation Damage, Canadian Journal of Civil Engineering, Vol. 1, 1974.
[52] Study of Air Injection into the Flow in the Boulder(Hoover) Dam Spillway Tunnels, USBR, Report. No. Hydl86. Oct. 1945.
[53]Wagner W. E. and Jabara M.A., Cavitation Damage Downstream from Outlet Works Gates, Proc. IAHR 14th Congress, Paris, Vol. 5, 1971.
[54]时启燧,掺气减蚀设施的研究与应用[J],泄水工程高速水流研究进展,1990年10月.
[55]冯家山水库泄洪洞通气减蚀原型观测研究报告[R],水力水电科学研究院、冯家山水库工程指挥部,陕西省水利水电勘测设计院、水利部西北水科所等,1980年10月.
[56]肖兴斌,王才欢,王业红,弧形闸门突扩跌坎式通气减蚀研究进展综述[J],长江科学院院报,2000年10月.
[57]П.A.伏依诺维奇,A.И.舒华兹,掺气水流的均匀运动[C],高速水流论文译丛,第1辑第1册,科学出版社,1958年.
[58] Lane, E.W., Entrainment on Spillway Face, Civil Enger, Vol.9, 1939.
[59] Halbronn, G., Durand, R. and G. Cohen de Lara, Air Entrainment in Steeply Sloping Flumes, Proc., Minnesota International Hydraulics Convention, 1953.
[60] Wood, I.R., Air Water Flows, 21st Congress IAHR, Mebourne, Australia, 1985.
[61] Bruschin, J., Forced Aeration of High Velocity Flows, Journal of Hydraulic Research, Vol.25, No.1, 1987.
[62] Chanson, H., A Model Study of Aerator Performance, Thesis Submitted to the University of Canterbury for the Degree Doctor of Dhilosophy(Civil Engieering), 1988.
[63] Pinto, N.L.de S. and Neidert, S.H., et al., Aeration at High Velocity Flows, Water Power & Dam Construction, Vol.34. Feb/March 1982.
[64] Rutschmann, P. and Hager W.H., Design and Performance of Spillway Chute Aerators, Water Power & Dam Construction, Vol.42, January 1990.
[65]潘水波等,通气挑坎射流的挟气能力[J],水利学报,1980年第5期.
[66]杨永森,挑坎型掺气槽过流掺气特性的研究[C],92全国水动力学研讨会论文集,1992年10月.
[67]陈长植,于琪洋,杨永森,挑坎型掺气减蚀设施过流掺气特性研究[J],水利水电技术,1999年第10期.
[68] Chanson,H., A Study of Air Entrainment and Aeration Devices on a Spillway Model, Ph.D.Thesis, Univ. of Canterbury, New Zealand, 1988.
[69] Chanson,H., Study of Air Demand on Spillway Aerator, J1 of Fluid Engrg., ASME, Vol.112, Sept.1990.
[70]黄建波,李士豪,倪汉根,掺气对空泡溃灭压力的影响[J],水利学报,1984年第4期.
[71]倪汉根,掺气减蚀机理和空腔长度、掺气量及保护长度计算方法的研究[R],高拱坝关键技术研究子题研究报告,大连理工大学,1992年11月.
[72]周菊华,水工建筑物掺气减蚀设施近况简介[J],云南水电技术,1991年第2期.
[73]时启燧,通气减蚀挑坎水力学问题的试验研究[J],水利学报,1983年第3期.
[74] Vischer D, et al. Hydraulic Modeling of Air Slots in Open Chute Spillway[J], Int1. Conf. On the Hydraulic Modeling of Civil Engineering Structures, BHRA Fluid Engineering, Coventry, UK, 1982.
[75]杨永森,杨永全,掺气减蚀设施体型优化研究[J],水科学进展,2000,11(2).144-147.
[76]聂孟喜.掺气折流器对侧空腔和底空腔长度的影响[J].水利学报,2002,(5):91-96.
[77]周赤,韩继斌,肖兴斌,弧门突扩跌坎掺气减蚀应注意的问题[J],水电工程研究,1997年3月:29-36.
[78]肖兴斌,王业红,弧门突扩跌坎式通气减蚀研究应用综述,[J],中南水力发电,2001年12月:65-69.
[79]庞昌俊.大型“龙抬头”明流泄洪洞小底坡掺气减蚀设施的选型研究[J].水利学报,1993,(6):61-66.
[80]王海云,高水头龙抬头泄洪洞掺气减蚀试验研究及数值模拟,四川大学硕士论文,2004年.
[81]孙双科,柳海涛,王晓松,姜涵,缓坡条件下凹型掺气坎布置形式研究[C],水力学与水利信息学进展,2003年.
[82]黄委会设计院技术处,掺气减蚀原理与应用[M],1990年12月.
[83] Rutschmann, P. and Hager, W.H., Air Entrainment by Spillway Aerators, Journal of Hydraulic Engineering, ASCE, Vol.116, June, 1990.
[84]林炳尧,许协庆,重力场中二维空腔流动的有限元分析[J],应用数学和力学,1985年第5期.
[85]杨永森,吴持恭,二维空腔流动的一种新的数值模拟方法[J],水动力学研究与进展,A辑,增刊,1992年12月.
[86] Yuan, M., On Numerical Simulations of Aerated Jet Flows about Aerators on Spillways, 7th Congress APD-IAHR, Nov., 1990, Beijing.
[87]杨永森,强迫掺气水流的数学模型[R],清华大学博士后出站报告,1993年7月.
[88]徐一民王韦许唯临刘善均,掺气坎(槽)射流空腔长度的计算[J],水利水电技术,2004,35(10).7-9.
[89]杨永森,杨永全,帅青红,低Fr数流动跌坎掺气槽的水力及掺气特性[J],水利学报,2000(2).27-31.
[90] Pinto, N.L. de S., Designing Aerators for High Velocity Flow, Water Power & Dam Construction, Vol. 41, July 1989.
[91] Bruschin, J., Hydraulic Modelling at the Piedra del Aguila Dam, Water Power & Dam Construction, Vol. 37, Jan 1985.
[92]杨永森,陈长植,于琪洋,掺气槽上射流挟气量的数学模型[J],水利学报.1996(3).13-31.
[93]陈先朴,西汝泽,邵东超,柴恭纯,掺气减蚀研究的新方向[J],水利水电技术,2001年第10期.
[94]黄国强,三峡工程溢流坝掺气减蚀研究[J],中国三峡建设,1997年3月,15-18.
[95]吴持恭,明槽自掺气水流的研究[J],水力发电学报,1988年第4期.
[96]杨永森,明渠自掺气水流掺气浓度分布Wood模型的改进研究[J],四川水力发电,1992年第2期.
[97]周建军,明渠自掺气水流掺气浓度分布研究[J],水动力学研究与进展,1993年9月.
[98]崔陇天,掺气挑坎下游含气浓度分布[J],水利学报,1985年第1期.
[99]杨永森,吴持恭,通气槽挑射水流掺气特性的研究[J],水利学报,1992年第4期,1-7.
[100]苑明顺,掺气槽下游二维含气浓度分布计算[J],水利学报,1991年第12期,9-16.
[101]罗铭,掺气减蚀设施后沿程掺气浓度数学模型[J],水利学报,1987年第9期.
[102] Xu, W. L. and Jin, Z. Q., Numerical Model for the Computation of Unsteady Bubbly Turbulence Flow in an Open Channel, eth Int. Symp. on Refined Flow Modeling and Turbulence Measurements, Wuhan, China, 1990.
[103]赵文华,几种典型水气两相流动问题的理论分析及数值模拟[D],成都科技大学博士论文,1992年7月.
[104] Zarrati A. R. Mathematical Modeling of Air-water Mixtures in Open Channels. Journal of Hydraulic Research, 1994, 32(5), 713-714.
[105]谭立新,许唯临,杨永全,明渠水气两相流数值模拟[J],四川联合大学学报(工程科学版)1999年1月,93-97.
[106]谭立新,许唯临,杨永全,水气二相流特点及其单流体模型[J],西安理工大学学报,2000年第3期,280-283.
[107]杨永全,现代工程水力学,西南民族学院学报(自然科学版)[J],2001年第3期,253-257.
[108]潘水波,挑坎射流挟气量试验的缩尺影响[C],水利水电科学研究院科学研究论文集第26集,水利电力出版社,1985年.
[109] Pinto, N.L.de S. and Neidert, S.H., Modeling Aerator Devices Dimensional Considerations, Proceedings of XXII Congress IAHR, Switerland, 1987.
[110]夏毓常,张黎明,水工水力学原型观测与模型试验[M],北京,中国电力出版社,1999,105-108.
[111] Bruschin J. Aeration Offsets for Spillway Chutes and Bottom Outlets, In: Proceedings of Symp. on Scale Effects in Modeling Hydraulics Structures, 1984.
[112] Wang Shixia, The Air Entraining Capacity of Supercritical Flow Over an Aeration Ramp and the Scale Effect Upon it. In: Proceedings of Int. Symp. on Hydraulic Research in Nature and Laboratory Vol. 1, 1992, 132-137.
[113]刘大明,高流速水工建筑物上掺气槽通气量的水力模拟[J],长江科学院院报,1995年3月,1-8.
[2] Knapp.Daily.Hammitt.Cavitation.McGraw—Hill.1970.(中译本.空化与空蚀。水利出版社.1981年) .
[3]郭军等.大型泄洪洞高速水流的研究进展及风险分析[J].水力学报.2006年第10期.
[4]吴持恭,高速水力学学科发展综述[J],泄水工程高速水流研究进展,1990,年10月.
[5] Besant,H.W., Hydrostatics and Hydro dynamics, Art.158, Cambridge University Press, London, 1859.
[6] Rayleigh, L., On the Pressure Developed in a Liquid During the Collapse of a Spherical Cavity, Phil. Mag. Vol.34, 1917.
[7] Plesset, M.S., The Dynamics of Cavitation Bubbles[J], Trans. AS ME, J.Appl. Mech., vol.16, 1949.
[8] Gilmore, F.B., The Growth and Collapse of a Spherical Bubble in a Viscous Compressible Liquid, Calif. Inst. of Tech., Hydrodyn. Lab., Rep. 26-4, 1952.
[9] Benjamin, T.B., Pressure Waves From Collapsing Cavity, 2nd Symp. Naval Hydrodyn., Washington D.C., 1958.
[10] Hunter, C., On the Callapse of An Empty Cavity in Water, J. Fluid Mech., Vol.8, 1960.
[11] Hickling, R., Plesset, M.S., Collapse and Rebound of A Spherical Bubble in Water, Phys. Fluids, Vol.7, 1964.
[12] Jahsman, W.E., Collapse of A Gas-Filled Spherical Cavity, J. Appl. Mech., vol.35, 1968.
[13] Plesset, M.S., Prosperetti, A Bubble Dynamics and Cavitation, Annual Revew. of Fluid Mech., Vol.9, 1977.
[14] Naude, C.F., Ellis, A.T., On the Mechanism of Cavitation Damage by Nonhemispherical Cavities Collapsing in Contact with a Solid Boundary, Trans ASME, J. Basic Engr., Vol.83, 1961.
[15] Van wijingaarden, L., On the Collective Collapse of A Large Number of Gas Bubbles in Water, Proc. 11th Int. Congr. of Appl. Mech., Springer, Berlin, 1964.
[16] Chahine, G.L., Asymptotic Theory of Collective Bubble Growth and Collapse, Proc. 5th Int. Symp. On Water Column Separation, Obernach, Germany, 1981.
[17] Morch, K.A., Cavity Cluster Dynamics and Cavitation Erosion, Report of Appl. Phy. Lab., Technical University of Denmark, DK-2800, Lyngby, Denmark, 1982.
[18]黄建波,初生空化数及空化荷载的预测[D].博士论文,大连理工大学,1987年9月.
[19] Plesset, M.S., Chapman, R.B., Collapse of An Initially Spherical Vapor Cavity in the Neighbourhood of A Solid Boundary, J.Fluid Mech., Vol.47, 1971.
[20] Mitchell, T.M & Hammitt, F.G. Asymmetric Cavitation Bubble Collapse [J]. Trans. ASME, J.Fluids Eng. 1973, 95,29-37.
[21] Guetti,L., Lucca.G & Prosperetti A. A Numerical Method for the Dynamics of Non-spherical Cavitation Bubbles. In Proceedings of the 2nd International colloquium on drops and bubbles[C],1981,175-181.
[22]陆力,许协和,固液两项流体中刚性平面边壁附近的空泡溃灭计算[J],水动力学研究与进展,1990年12月,106-119.
[23]蔡悦斌,鲁传敬,何友声,瞬态空化泡的成长与溃灭[J],水动力学研究与进展,1995年12月,653-660.
[24]丁志杰,张慧生,数值模拟气泡在粘性液体中上升运动的Euler-Lagrange方法[J],复旦大学学报自然科学版,1999,Vol 038,No002,146-152.
[25]严育兵,边界积分法的若干问题和近壁空化气泡表面张力效应的数值研究[D],复旦大学博士论文,2002.
[26] R.T.Knapp, J.W.Daily, and F.G. Hammitt,“Cavitation”,McGraw Hill Book Book Co., 1970.中译本“空化与空蚀”[M],水利水电科学研究院译,水利出版社,1981年.
[27] F.E. Fox and K.F. Herzfeld,“Gas Bubbles with Organic Skin as Cavitation Nuclei”, Jr. Acoust. Soc. Am. 26, 1954.
[28]常近时,寿梅华,于希哲,“水轮机运行”[M],水利电力出版社,1983年.
[29] E.N.Harvey, W.D.McElroy and A.H. Whiteley,“On Cavity Formation in Water”, Jr. Appl. Phys., 18, No.2, 1947.
[30] Hall, J.W., The Inception of Cavitation on Isolated Surface Irregularies, Trans. ASME, Basic Engr. Vol.82, 1960.
[31] Arakeri, V.H., Acosta, A.J., Viscous Effects in the Inception of Cavition on Axisymmetric Bodies, Fluids Engr., Trans ASME, Vol.95, 1973.
[32] Katz, J., Cavitation Phenomena with Regions of Flow Separation, J.Fluid Mech., Vol.140, 1984.
[33] Keller, A.P., Cavitation Investigations at Model Body Families as A Contribution to the Classification of Scale Effects at Cavitation Inception, Int. Symp. on Hydraulics for High Dam, Beijing, Nov. 1988.
[34]何子干,紊流场的计算及初生空化数的理论预测[D],博士论文,大连理工大学,1988年8月.
[35]杨庆,空化初生机理及比尺效应研究[D],博士论文,四川大学,2005年5月.
[36] M.Kornfeld and L.Suvarov,“On the Destructive Action of Cavitation”, Jr.Appl.phys., 15,1944.
[37] M.Rattray,“Perturbation effects in Cavitation Bubble Dynamics”, Ph.D.thesis Calif Inst. Of Technology, Pesadena, Calif, 1951.
[38] C.F.Kling and F.G.Hammitt,“A Photograph Study of Spark Induced Cavitation Bubble Collapse”, Trans. ASME, J. Basic. Engr., Vol.94, Ser. D., No.4, Dec. 1972.
[39] W.Lauterborn and H. Bolle,“Experimental Investigations of Cavitation Bubble Collapse in the Neighbourhood of a Solid Boundary”, J. Fluid Mech, Vol.72, No.2,1975.
[40] A.Shima, K.Takayama and Y.Tomita,“Mechanisms of the Bubble Collapse Near a Solid Wall and the Induced Impact Pressure Generation”, Rep Inst. High Speed Mech. Vol. 48,1984.
[41] A.T.Ellis,“Production of Accelerated Cavitation Damage by an Acoustic Field in a Cylindrical Cavity”, Jr. Acoust. Soc. Am., 27, 1965.
[42] G.Petracchi,“Investigations of Cavitation Corrosion”, Metallurgia Italiana, 4l, No. 1, 1949.
[43] M.S.Plesset,“Bubble Dyramics”, in R. Davies (ed.), Cavitation in Real Fluids, Elsevier Publishing Co., Amsterdam. 1964.
[44] W.S.汉密尔顿,水工建筑物气蚀破坏与防护[J],中南水电,1989年第3期.
[45]熊贤禄,傅佩芬整理,美国专家布格和蒋赛延关于二滩水电站水力学问题的发言(综合整理)[J],水电工程研究,1983(1).
[46]溢洪道设计规范[S],SL253-2000.
[47] Mousson J.M., Pitting Resistance of Metals Under Cavitation Conditions, Trans, ASME, 59,1937.
[48] Vuskovic I., Recherches Concernant L′inbluenc de la Teneur en Air la Cavitation et la Corrosion, Bulletin Escher-Wyss, Tom. 13, 1940.
[49] Peterka A.J., The Effect of Entrained Air on Cavitation Pitting, Proc. IHR Minnesota, 1953.
[50] Rasmussen R.E.H., Some Experiments on Cavitation Erosion in Water mixed with Air, Proc. NPI. Sympoaium on Cavitation in Hrdrodynamics, Paper 20, London. 1956.
[51] Russell S.O. and Sheehan G.J., Effect of Entrained Air on Cavitation Damage, Canadian Journal of Civil Engineering, Vol. 1, 1974.
[52] Study of Air Injection into the Flow in the Boulder(Hoover) Dam Spillway Tunnels, USBR, Report. No. Hydl86. Oct. 1945.
[53]Wagner W. E. and Jabara M.A., Cavitation Damage Downstream from Outlet Works Gates, Proc. IAHR 14th Congress, Paris, Vol. 5, 1971.
[54]时启燧,掺气减蚀设施的研究与应用[J],泄水工程高速水流研究进展,1990年10月.
[55]冯家山水库泄洪洞通气减蚀原型观测研究报告[R],水力水电科学研究院、冯家山水库工程指挥部,陕西省水利水电勘测设计院、水利部西北水科所等,1980年10月.
[56]肖兴斌,王才欢,王业红,弧形闸门突扩跌坎式通气减蚀研究进展综述[J],长江科学院院报,2000年10月.
[57]П.A.伏依诺维奇,A.И.舒华兹,掺气水流的均匀运动[C],高速水流论文译丛,第1辑第1册,科学出版社,1958年.
[58] Lane, E.W., Entrainment on Spillway Face, Civil Enger, Vol.9, 1939.
[59] Halbronn, G., Durand, R. and G. Cohen de Lara, Air Entrainment in Steeply Sloping Flumes, Proc., Minnesota International Hydraulics Convention, 1953.
[60] Wood, I.R., Air Water Flows, 21st Congress IAHR, Mebourne, Australia, 1985.
[61] Bruschin, J., Forced Aeration of High Velocity Flows, Journal of Hydraulic Research, Vol.25, No.1, 1987.
[62] Chanson, H., A Model Study of Aerator Performance, Thesis Submitted to the University of Canterbury for the Degree Doctor of Dhilosophy(Civil Engieering), 1988.
[63] Pinto, N.L.de S. and Neidert, S.H., et al., Aeration at High Velocity Flows, Water Power & Dam Construction, Vol.34. Feb/March 1982.
[64] Rutschmann, P. and Hager W.H., Design and Performance of Spillway Chute Aerators, Water Power & Dam Construction, Vol.42, January 1990.
[65]潘水波等,通气挑坎射流的挟气能力[J],水利学报,1980年第5期.
[66]杨永森,挑坎型掺气槽过流掺气特性的研究[C],92全国水动力学研讨会论文集,1992年10月.
[67]陈长植,于琪洋,杨永森,挑坎型掺气减蚀设施过流掺气特性研究[J],水利水电技术,1999年第10期.
[68] Chanson,H., A Study of Air Entrainment and Aeration Devices on a Spillway Model, Ph.D.Thesis, Univ. of Canterbury, New Zealand, 1988.
[69] Chanson,H., Study of Air Demand on Spillway Aerator, J1 of Fluid Engrg., ASME, Vol.112, Sept.1990.
[70]黄建波,李士豪,倪汉根,掺气对空泡溃灭压力的影响[J],水利学报,1984年第4期.
[71]倪汉根,掺气减蚀机理和空腔长度、掺气量及保护长度计算方法的研究[R],高拱坝关键技术研究子题研究报告,大连理工大学,1992年11月.
[72]周菊华,水工建筑物掺气减蚀设施近况简介[J],云南水电技术,1991年第2期.
[73]时启燧,通气减蚀挑坎水力学问题的试验研究[J],水利学报,1983年第3期.
[74] Vischer D, et al. Hydraulic Modeling of Air Slots in Open Chute Spillway[J], Int1. Conf. On the Hydraulic Modeling of Civil Engineering Structures, BHRA Fluid Engineering, Coventry, UK, 1982.
[75]杨永森,杨永全,掺气减蚀设施体型优化研究[J],水科学进展,2000,11(2).144-147.
[76]聂孟喜.掺气折流器对侧空腔和底空腔长度的影响[J].水利学报,2002,(5):91-96.
[77]周赤,韩继斌,肖兴斌,弧门突扩跌坎掺气减蚀应注意的问题[J],水电工程研究,1997年3月:29-36.
[78]肖兴斌,王业红,弧门突扩跌坎式通气减蚀研究应用综述,[J],中南水力发电,2001年12月:65-69.
[79]庞昌俊.大型“龙抬头”明流泄洪洞小底坡掺气减蚀设施的选型研究[J].水利学报,1993,(6):61-66.
[80]王海云,高水头龙抬头泄洪洞掺气减蚀试验研究及数值模拟,四川大学硕士论文,2004年.
[81]孙双科,柳海涛,王晓松,姜涵,缓坡条件下凹型掺气坎布置形式研究[C],水力学与水利信息学进展,2003年.
[82]黄委会设计院技术处,掺气减蚀原理与应用[M],1990年12月.
[83] Rutschmann, P. and Hager, W.H., Air Entrainment by Spillway Aerators, Journal of Hydraulic Engineering, ASCE, Vol.116, June, 1990.
[84]林炳尧,许协庆,重力场中二维空腔流动的有限元分析[J],应用数学和力学,1985年第5期.
[85]杨永森,吴持恭,二维空腔流动的一种新的数值模拟方法[J],水动力学研究与进展,A辑,增刊,1992年12月.
[86] Yuan, M., On Numerical Simulations of Aerated Jet Flows about Aerators on Spillways, 7th Congress APD-IAHR, Nov., 1990, Beijing.
[87]杨永森,强迫掺气水流的数学模型[R],清华大学博士后出站报告,1993年7月.
[88]徐一民王韦许唯临刘善均,掺气坎(槽)射流空腔长度的计算[J],水利水电技术,2004,35(10).7-9.
[89]杨永森,杨永全,帅青红,低Fr数流动跌坎掺气槽的水力及掺气特性[J],水利学报,2000(2).27-31.
[90] Pinto, N.L. de S., Designing Aerators for High Velocity Flow, Water Power & Dam Construction, Vol. 41, July 1989.
[91] Bruschin, J., Hydraulic Modelling at the Piedra del Aguila Dam, Water Power & Dam Construction, Vol. 37, Jan 1985.
[92]杨永森,陈长植,于琪洋,掺气槽上射流挟气量的数学模型[J],水利学报.1996(3).13-31.
[93]陈先朴,西汝泽,邵东超,柴恭纯,掺气减蚀研究的新方向[J],水利水电技术,2001年第10期.
[94]黄国强,三峡工程溢流坝掺气减蚀研究[J],中国三峡建设,1997年3月,15-18.
[95]吴持恭,明槽自掺气水流的研究[J],水力发电学报,1988年第4期.
[96]杨永森,明渠自掺气水流掺气浓度分布Wood模型的改进研究[J],四川水力发电,1992年第2期.
[97]周建军,明渠自掺气水流掺气浓度分布研究[J],水动力学研究与进展,1993年9月.
[98]崔陇天,掺气挑坎下游含气浓度分布[J],水利学报,1985年第1期.
[99]杨永森,吴持恭,通气槽挑射水流掺气特性的研究[J],水利学报,1992年第4期,1-7.
[100]苑明顺,掺气槽下游二维含气浓度分布计算[J],水利学报,1991年第12期,9-16.
[101]罗铭,掺气减蚀设施后沿程掺气浓度数学模型[J],水利学报,1987年第9期.
[102] Xu, W. L. and Jin, Z. Q., Numerical Model for the Computation of Unsteady Bubbly Turbulence Flow in an Open Channel, eth Int. Symp. on Refined Flow Modeling and Turbulence Measurements, Wuhan, China, 1990.
[103]赵文华,几种典型水气两相流动问题的理论分析及数值模拟[D],成都科技大学博士论文,1992年7月.
[104] Zarrati A. R. Mathematical Modeling of Air-water Mixtures in Open Channels. Journal of Hydraulic Research, 1994, 32(5), 713-714.
[105]谭立新,许唯临,杨永全,明渠水气两相流数值模拟[J],四川联合大学学报(工程科学版)1999年1月,93-97.
[106]谭立新,许唯临,杨永全,水气二相流特点及其单流体模型[J],西安理工大学学报,2000年第3期,280-283.
[107]杨永全,现代工程水力学,西南民族学院学报(自然科学版)[J],2001年第3期,253-257.
[108]潘水波,挑坎射流挟气量试验的缩尺影响[C],水利水电科学研究院科学研究论文集第26集,水利电力出版社,1985年.
[109] Pinto, N.L.de S. and Neidert, S.H., Modeling Aerator Devices Dimensional Considerations, Proceedings of XXII Congress IAHR, Switerland, 1987.
[110]夏毓常,张黎明,水工水力学原型观测与模型试验[M],北京,中国电力出版社,1999,105-108.
[111] Bruschin J. Aeration Offsets for Spillway Chutes and Bottom Outlets, In: Proceedings of Symp. on Scale Effects in Modeling Hydraulics Structures, 1984.
[112] Wang Shixia, The Air Entraining Capacity of Supercritical Flow Over an Aeration Ramp and the Scale Effect Upon it. In: Proceedings of Int. Symp. on Hydraulic Research in Nature and Laboratory Vol. 1, 1992, 132-137.
[113]刘大明,高流速水工建筑物上掺气槽通气量的水力模拟[J],长江科学院院报,1995年3月,1-8.